What is the inverse of f(x)=sqrt((e^x-4)/(3-e^x)) ?

The inverse of f(x)=sqrt((e^x-4)/(3-e^x)) is ln(-(-4-3x^2)/(x^2+1))

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inverse of f(x)=sqrt((e^x-4)/(3-e^x))

inverse

f (x) = \frac{e ^{x} - 4}{3 - e ^{x}}

ln (- \frac{- 4 - 3 x ^{2}}{x ^{2} + 1})

Solution steps

y = \frac{e ^{x} - 4}{3 - e ^{x}}

Replace

x

with

y

x = \frac{e ^{y} - 4}{3 - e ^{y}}

Solve for

y, x = \frac{e ^{y} - 4}{3 - e ^{y}}

ln (- \frac{- 4 - 3 x ^{2}}{x ^{2} + 1})

f (x) = \frac{x + 2}{1 + x}

- cos (2 x)

f (x) = - 2 x^{7} - 2

f (x) = 2 x + 4 + x^{2}

f (x) = x^{2} - 9 x + 20

What is the inverse of f(x)=sqrt((e^x-4)/(3-e^x)) ?
The inverse of f(x)=sqrt((e^x-4)/(3-e^x)) is ln(-(-4-3x^2)/(x^2+1))